Música Brasilis

Preface to the first edition

 

Alongside the transformations which occurred in the harmonic language of Western classical music of the 20^thcentury, from the growing dilation of tonality up to its total weakening and the emergence of a new free language, rhythmic structures went through a similar process, gradually breaking the tyranny of the measure through the agogic independence of melodic phrasing - already explored in works of Brahms and other Romantic composers of the 19^thcentury - attaining polyrhythms, alternated rhythms and the complete abolition of mensuralism.

It is difficult to establish causes and effects between the trajectories in the development of melodic-harmonic contents and rhythm. Certainly, both are the consequence of the evolution of musical thinking, which, when combined with the development of new technologies in the late 20^thcentury, climaxed with the freedom from the physical-acoustic generation of sound.

Different from Schoenberg's proposal of a new organization of musical language with his serial system, Almeida Prado did not set out to come up with a new organization of rhythmic structures, but only to catalogue in the form of a workbook the main rhythmic configurations which emerged during the process of the liberation from the 17^thcentury melodic quadrature.

As a matter of fact, there was no one better for the job: his own musical creation is itself a vast showcase of rhythmic invention, a product of a fruitful imagination, in rhythmic, melodic, harmonic and expressive terms. Such fertile imagination commonly sends shivers down his interpreters' spines after they see the complexity of the metric and rhythmic structures in his scores. However, after a quieter, closer study, their execution comes through fluently and naturally, which demonstrates not only that Almeida Prado's musical thinking comes before what apparently are only mathematical convolutions, but also that he is a true master.

His Cartilha Rítmica para Piano(Primer of Rhythm for Piano)invites us on a musical journey through the myriad possibilities of rhythmic and metric articulations practiced in 20^thcentury music, including in his own work. However, it should be emphasized that in these playful exercises the musical idea is always the determining factor, and that they were only written as a means to best attain the initial creative impulse.

The exercises were created to consider all technical resources on the piano. Yet they are much more than a simple tool for students to simply reproduce multiple rhythmic structures, isorhythmic figurations, alternations between strict and free tempos, fixed pulses displaced by irregular accents, spatialization of intervals and rhythms, combinations of syncopations and tuplets in free-flowing rhythms, as well as different time signatures, from the simplest (such as 2/4) to the most unusual (10/16, 11/16, 13/16, 7/8, 4/8, 5/2, 15/32, 19/8, etc.).

Prado's inexhaustible creative imagination also offers a summary of techniques and languages used in Western music, from Gregorian to Renaissance music, from Bachian inventions to the march honoring Gottschalk, from Czerny's exercises to the birds of Messiaen, his master. In addition, the work always reflects his strong personality, which brings these multiple languages together in complete harmony, from tonal triads to politonal superpositions, to the free structures that characterize a large portion of 20^th-century music, frequently infused with the religiosity that marks his life and work.

Moreover, the universality of his exercises is amplified by his fascinating re-reading of the rhythms of non-European cultures, such as African-Brazilian and Hindu. 

Frequently, as a consequence of conventional academic training, piano students are not familiar with popular rhythms, and are unable to improvise or play popular music by ear. In the Cartilha, students - including Brazilian students - will find an extremely musical and helpful introduction to Brazilian rhythms and popular music styles, such asmaracatu, frevo, baião, caboclinhos, and other African-Brazilian rhythms from Bahia, as well as the batucada, which the author defines as the “celebration of all rhythms.”

Like the exercises on African-Brazilian rhythms, the exercises on Hindu rhythms and modes are not just a musicological compilation of rhythmic prototypes, but a creative reevaluation of primary sources, through which the educational goal of the collection is attained.

The creative work of Almeida Prado in the book is undoubtedly admirable, and its educational reach and musical beauty deserve to be better known. The Cartilha should be used by music schools, teachers and students, composers and interpreters, from all parts of the world.

The editorial work of these two musicians - pianist Sara Cohen and musicologist/pedagogue Salomea Gandelman - is also worthy of praise. They reviewed and edited the scores and contributed invaluable text essential to the understanding of the musical and technical content of the exercises.

The excellent recordings of a large number of the exercises are brilliantly executed by Sara Cohen. Her perfect technique and musical fluency are always in evidence, making fascinating music out of the most complex rhythmic figures.

 

Rio de Janeiro, December 24^th, 2005

 

Edino Krieger 

 

 

Foreword

 

The Cartilha Rítmica para Piano(Primer of Rhythm for Piano) was conceived and composed by José Antonio Rezende de Almeida Prado (1943-2010) virtually in its totality in the 1990s. Sponsored by the Cultural department of Petrobras, supported by the Incentive to Culture Law of the Culture Ministry, the first edition was made public in 2005 as a printed book. This contained the revised and edited compositions (under the Author’s supervision): texts that introduce the reader to the composer, to the Primerand to the rhythmic modern conceptions contained in the work, a short analysis of the 103 exercises, an account of articles and theses on the piano work of Almeida Prado as well as a CD (recorded by Sara Cohen) focusing on the majority of the exercises.

The excellent reception to the Primer, precious material not only to pianists, but also to students and teachers of musical theory, musical perception and appreciation, analysis, composition and musicologists in general has led us to consider that this work deserved to have a new revised and enlarged publication. Preserving the original spirit of the project, i.e., to propose an articulation between the printed material  and its sound rendering and the general theory of music, we found in the project Musica Brasilis () the space for the display and availability of the Primer.

Almeida Prado left us before achieving his goal, expressed in the letter printed at the end of this book, of extending the Primerto other instruments.  To our delight, this has been realized by graduation and post-graduation students. The composer, who was a much loved teacher, would certainly feel happy and proud seeing the extension of his work.

Our objective remains the same as expressed in this book’s first edition: that this material should stimulate people’s curiosity to listen and seek deepening knowledge of the various compositional strategies contained in pieces composed in following years and also that it should help in the achievement of the required skills to solve issues of performance and the development of the creative process.

We are particularly grateful to Abrahão Brafman and Marisa Gandelman to all who encouraged the new publication of the Prime,particularly our students and readers who were so enthusiastic about this work.

 

 

 

Rio de Janeiro, novembro de 2017

Salomea Gandelman

Sara Cohen

 

 

The composer and the work

 

The composer

 

José Antônio Rezende de Almeida Prado (Santos/São Paulo, 2/8/1943 - São Paulo/ São Paulo, 11/21/2010) is considered one of Brazil's most representative and praised composers. A disciple of Dinorá de Carvalho, Camargo Guarnieri, Osvaldo Lacerda and Gilberto Mendes, in Brazil, and Nadia Boulanger, Olivier Messiaen and Annette Dieudonnée, in Paris between 1969 and 1973, Almeida Prado produced a rich, expressive and varied body of work. Parallel to his intense activities as a composer, he was also the director of the Cubatão Municipal Conservatory (in 1973), professor of composition and analysis of the Department of Music in the Arts Institute of Campinas State University (1975 through 2000) and guest professor of the Music Department of the University of Indiana (in 1984) and the Rubin Academy of Jerusalem (1989 and 1990), having granted chair #15 (Carlos Gomes's), 1972, at the Brazilian Academy of Music. His work includes compositions for many formations, including orchestra, voices and choir (Pequenos funerais cantantes, 1969); orchestra, piano and brass quintet (Aurora, 1975); orchestra (Sinfonia Unicamp, 1976 and Sinfonia dos orixás, 1985-1986); two pianos and symphonic band (Cartas Celestes VII, 1998); violin and orchestra (Concerto, 1999); violin and string orchestra (Concerto, 1976); piano, flute and string quartet (Portrait de Lili Boulanger, 1972); soprano, narrator, piano and percussion (Carta de Jerusalém 1973); ten-string viola caipira(Sertões, 1978); saxophone and piano (230 East, 51^th, New York, 1983); five flutes (Livro de Oxóssi, 1986); violin and piano (Sonata n^o3, 1991); two acoustic guitars (Sonata tropical, 1996); voice and piano (Quatro poemas de Manuel Bandeira, 1998, and many others); and solo piano, the instrument of the composer. As a pianist, he mastered many technical resources and a rich array of timbres and wrote a vast literature for the instrument.

The list of awards he was granted is also extensive, and the following should be highlighted: at the Guanabara Festival of Music (for Pequenos funerais cantantes, 1969), by the Music Commission of the state of São Paulo (for the oratorio Trajetória da independência, 1972), by the Goethe Institute, together with the Brazilian Society of Contemporary Music (for Magnificat, for a cappellachoir, and Livro sonoro, for a string quartet, 1973), by the São Paulo Association of Art Critics (for the Concerto para violino e orquestra de cordas, 1976, and the Noturno nº 13 para piano e violino, 1993), by the São Paulo State government (which granted him the Mario de Andrade Medal in 1979), by Funarte (a national award for his body of work, in 1995), at the 9^thFrancesc Civil de Girona International Competition (Cantares dos sem nome e de partidas, for soprano and strings, 1996), by the Government of the State of São Paulo (which granted him the Guarani Trophy and the Carlos Gomes Award for his body of work in 2000), by the Vitae Foundation (Concerto para oboé e cordasand Cartas Celestesn^os13 e 14, 2001) and, more recently, in 2005, by the Ministry of Culture (the Culture Merit Medal).

His compositions, influenced by the nationalistic esthetic of Mário de Andrade and Guarnieri, are universal (atonal, serialist, dodecaphonic-serialist, transtonal) and post-modern (with collages, citations and a Romantic form, such as nocturnes, ballads and preludes), reaching a personal synthesis, mostly through an exploration of free tonalism. Even in his Guarnierian phase - or after he left his master in search for new musical paths - his most distinct styles were already noticeable: a large variety of timbres, interval spatialization, a rich palette of intensities (from 5pto 4f), tremolos and clusters, dense and mixed textures, great resonances, complex rhythms, a combination of modalism, tonalism and atonalism, and the full range of the keyboard.

Almeida Prado was not prone to making abstract music. Even when he was experimenting with different sounds or forms, his poiesisemerged from a folk theme, a poem, a religious experience, from his interest in the mythic-telluric world, from feelings, impressions and fantasies, all of which are processed and converted into musical streams with extreme sensibility. His ubiquitous concern with timbre - which he associates with colors, textures and spatialization - made him a pictorial, poetic and neo-impressionist composer whose verbal suggestions ("luminous," "mushy," "solar," "igneous," "nocturnal," "fulgent," "translucent like dawn", "like a spiral of fire", "granitic," "stellar", "like a morning washed by rain," "incandescent," "screaming like an anvil of fire" and many others) invite players to use their imagination, to listen and seek their own touch and sound.

 

Pedagogical approaches

 

The study of Almeida Prado's Cartilha rítmica para piano(Primer of Rhythm for Piano) shows how invaluable the book is for the understanding of rhythmic issues in 20^th-century music. Little by little, we were struck by the pertinence and intelligence of the composer's choice of exercises. In the following paragraphs, we will try to demonstrate their educational potential.

Organized into four different volumes with progressive exercises, mostly written between 1992 and 1999, the Cartilhaalso includes some pieces that were already familiar to piano scholars and admirers of his work, such as Ad laudes matutinas(1972); O canto das savanas(1983), from Savanas; Momentos 14 and19, from his 3^oCaderno de Momentos (1974); the 5^thvariation of Ta'aroá(1971), and an excerpt of Nebulosa NGC 696095, from Carta Celeste n^o1. In the introduction for Volume I - which would later become Volume II - entitled "Quick explanation," Almeida Prado tells us that, at first, his goal was only to compile "a few studies that systematically explored problems in piano technique." He gave that up, however, concluding that he had already done that with his 55 Momentos, written between 1965 and 1983, according to the author’s words. He then thought of writing a "present-day Czerny," but focusing especially on rhythm.

In the first half of the 20^thcentury, dissonance broke free from any restraint as the force of the tonal system dissipated. Rhythmically, the regularity of pulses and meters was destabilized by constant changes in time signatures, articulations and tempos, irregular accentuations, syncopations, additive rhythms, polyrhythms, and polymeters, continuous disturbances accompanied by different clusters and resonances which stimulated the ears and triggered the imagination of players.

These are the issues Almeida Prado is dealing with. Each of his exercises addresses predominantly one of them (described in its title), although other, underlying issues are also considered. Simultaneously, despite exhibiting the nature and characteristics of the genre “exercise”, which implies the repetition of patterns designed to produce cognitive and motor development, most are also beautiful pieces that deserve inclusion in the concert repertoire. Through them, Almeida Prado clearly demonstrates not only that he masters his art, but also his talent as a piano teacher. That was not a new talent, since he was a distinguished pianist who, in his teaching of the instrument, addressed complex and relevant issues for contemporary music.

Even though the title and subtitle of the book (Primer of Rhythm for Piano: progressive exercises) speak for themselves and clearly communicate what the exercises are about, we decided to study the methodology behind Almeida Prado's pedagogical process. A systematic evaluation of all exercises allowed us to identify the different rhythmic formulations suggested by Almeida Prado, as well as analyze his pianistic solutions. Significantly, his take on each problem includes a combination of both the traditional and the new. The rhythmic practice of the "common practice period" is side by side in the Cartilhawith new possibilities for organizing pulse, meter and tempo. To study agility, scales, chords, dynamics, sonorities, polyphonies and pedalings, aspects which in traditional piano methods major and minor scales are used, Prado also includes Gregorian and Hindu modes, enigmatic, oriental and synthetic scales, as well as the exploration of resonance.

It is the eye of the piano professor who seeks to join the development of piano technique with the knowledge of compositional resources used by contemporary composers. This is done with great care: the exercises are developed with great economy of materials and rigorous pedagogical criterion. A high degree of complexity in one plain of the compositions is compensated with a relative lower degree in another; subtle and continuous elaborations whose underlying compositional procedures we cannot always grasp weave the exercises’s texture always maintaining the essence of the source material. Pianistically speaking, the composer wisely considered a few functional aspects of the human hand: successive groupings of neighboring tones, scales, arpeggios and fingerings in patterns developed with the shape of the hand in mind permit pianists to focus on the specific problems addressed by each exercise. This in turn facilitatesboth the performance and the comprehension of the specific rhythmic principles. Prado also offers important comments on how to study some of them.

Although the Cartilhaincludes the subtitle "progressive exercises" and is organized into volumes with different levels of difficulty established by the author, ranging from "easy" to "very difficult", both the title, the subtitle and the classification are arguable. The "very difficult" exercises are certainly a challenge, even for experienced pianists, but the "easy" and the "medium" assume good reading skills and motor coordination, that is, previously-acquired musical experience and technical control. It is true that one can learn to do things by doing them - a hard path to follow -, but it would be more efficient and economical to do a preparatory study and/or a parallel study with other pieces - for instance, those of Brazilian composers Osvaldo Lacerda, Ernst Widmer and Cláudio Santoro. Moreover, the title may suggest that it is a book "to learn how to read music" or "an elementary or rudimentary book on an art, science or doctrine," according to the dictionary definition. However, actually, it is about basic rhythmic issues explored by composers since the early 20^thcentury. The term "progressive," moreover, cannot be understood as a "pre-established order." It must be interpreted in a much richer, comprehensive manner, for a number of very important reasons which lie at the core of the teaching/learning process: adding a new element in each group of exercises; introducing groups of exercises with specific characteristics, that is, including new elements from one group to the other; and, last but not least, always being fresh, that is, using the musical vocabulary of the 20^thand 21^stcenturies. It is interesting to notice that Volume I introduces problems that may appear in later volumes, either under different or related titles, with a higher, or sometimes surprisingly lower degree of difficulty.

It is perhaps apt here to introduce Tillman and Swanwick's Spiral Model to explain and, simultaneously, evaluate the musical development of its different stages - materials, expression, form and value - which appear in the various musical activities expressed by the acronym C(L)A(S)P: Composition, Literature, Appreciation, Skills and Performance. The recursion or cyclicality (that is, the need to follow the Spiral at every contact with a new element, no matter what stage of musical development the musician is in), the cumulativeness (the idea that musical knowledge is formed by cumulative layers) and the pendular motion (with the polarity between the left, idiosyncratic and individual side, and the right, socially shared side of the Spiral, that is, the alternation between assimilation and accommodation, which indicate qualitative changes within the same stage of development), which are the pillars of the Spiral, can also be observed in the development of the Cartilha. As always, however, teachers who know their students need to suggest the most effective and feasible exercises for each one of them, as well as stimulate them to read others, following their preferences.

 

 

Twentieth century rhythmic strategies and the Cartilha rítmica para piano

 

One of the most important aspects of music in the 20^thcentury is the coexistence between pieces with rhythm and meter similar to those of the common practice period and pieces with totally innovative rhythmic strategies. Almeida Prado's Cartilha,in its four volumes, explores these strategies, many of which are very complex, although there is no intention of exhausting all possibilities.

It should be mentioned that all exercises in the Cartilhawere written using orthochronic notation. Only four pieces - Figures and accent marks with resonances(I.9), Interval and rhythmic spatialization(III.2), Increases and decreases around a pivot note (III.10) and Simultaneous tuplets(III.13) - and the third group of exercises of Hindu rhythms do not include explicit time signatures. This defines the rhythmic scope of the Cartilha, which led us to study its subjacent metric structures, superficial durational patterns and the interaction between them.

Some scholars use the relatively familiar rules in the metric structures of the tonal music of the common practice period as a starting point for addressing rhythm in 20^th-century music. The rhythmic structures used in that period are interpreted hierarchically as having isochronous pulses - whether explicit or implicit, at different speeds - and three different levels: a central level (with regular and recurring pulses); an inferior level (in which the isochronous durations - beat units - established by the central level are split into two or three parts); and a superior level (in which pulses are grouped into larger units). The recurrent pattern of strong and weak beats in the superior level is called meter. It can be duple or triple and remain almost invariable once established - which, in terms of notation, implies whole sections or pieces without time-signature changes.  Pulses in all hierarchic levels are synchronous, that is, all the pulses in the slow levels coincide with the strong pulses in the faster levels. Tempois also stable throughout the entire pieces or sections. Superficial or temporary metric changes are operationalized through syncopations, hemiolas, tuples’ and temporubat.

It is not by mere chance that metric regularity is one of the characteristics of tonal music, because it is through it that functional harmony and voice leading get part of their strength. The gradual dissolution of tonality that started in the late 19^thcentury ran parallel to the relaxation of the regularity and the ensuing flexibilitzation of barlines. The irregularity of rhythm and a gradual transformation of the other elements of musical discourse became increasingly employed.

There are several ways to operationalize structural irregularities under the norms of the common practice period: irregular grouping in all hierarchic levels, simultaneity of different meters (polymeters), asynchrony and controlled changes in speed and tempo. These strategies can be implemented simultaneously, producing structures that are complex both to write and to perform. In the next section we examine these aspects and illustrate them with exercises from the Cartilha.

 

 

Additive and divisive principles

 

There are two basic regulating principles frequently used to describe musical rhythm. The divisive principle, which is used in Western tonal music and predominates in the pieces of the common practice period, can be easily understood as a progress in even steps. In the hierarchical structure of measures, time is split into equal rhythmic units, which are also split in half and so on. In the additive principle, time is built by sequences of minimum rhythmic units, which produces groupings composed of long and short elements, such as 2+1, 3+3+2 or any other combination. In the additive principle, the focus is on what is added; in the divisive principle, the focus is on what is repeated.

The additive principle is used to describe asymmetric rhythms (those that cannot be divided in two equal parts) and irregular rhythms (those that use metric patterns that are not repeated), which are typical of the music produced after the common practice periodand of non-Western music. For instance, the 4/4 formula tells us that the four beats in each bar are represented by quarter notes or, if we dissolve them, eight eighth notes. There is regularity (time figures are repeated), homogeneity (time figures are all alike) and symmetry (each group can be split into two equal groups). The rhythmic pattern of a time signature like [3+3+2]/8, although it also includes eight eighth notes, can be split into three groups: the first two with three eighth notes and the last one with two. Therefore, there is no symmetry and homogeneity in what comes out of the coagulation of the eighth notes in each group, and the regularity takes place only at the level of the meter.

Exercise II.32 illustrates well this dialogue between the two principles: a fixed 4/4 time signature opposes a free time, in which the minimum reference figure - a sixteenth note - is grouped irregularly.

 

 

Regularly and irregularly varied groupings

 

If the metric structure of the common practice period is characterized by regular, constant groupings at the superior and inferior levels of the hierarchical structure, in the 20^thcentury many examples of regularly-varied groups of pulses (that is, pulse groups that vary in a regular pattern at the central level, such as 3+2, 3+2, 3+2 or 2+3+2, 2+3+2, 2+3+2) can be found. The most common way to write it is using a different numerator than those usually used in the common practice period. Numerators 5 - quintuple meters (II.6) - and 7 - septuple meters (II.7) - are used as frequently as numerators 2, 3, 4, 6, 9 and 12. Other numerators - such as 1, 8, 10 and 11 (II.11), among others - can also be found.

New terms and expressions arose to describe them, such as complex meters, asymmetric meters, additive meters, or even irregular or irrational meters. In our view, Scliar's terminology - primitive and derived meters - seem the most clear and all-encompassing. The primitive meters are the duple and triple meters. Their combination produces variations, both direct (when variations are composed of equal primitive meters) and indirect (of different primitive meters). For instance: quadruple meters are direct variations, and quintuple and septuple meters are indirect variations. However, although many efforts have been made to understand metric structure with a single terminology, we consider it best to analyze its groupings and their interrelations on all hierarchic levels.

Groups of pulses can also be irregularly varied, which produces metric structures in which changes do not follow a recurrent, periodical, constant pattern.

One way to notate changes - whether they are regular or irregular - in these groups is changing time signatures. Although this strategy is not exclusive of the 20^thcentury, it has been used much more widely since then than in the tonal era. Several terms have been used to designate it: alternating meters (when groups are regularly varied), changes in time signatures, variable meters and multimeters.

 

 

Perception and notation

 

Metric irregularities in the Cartilhacan often be predicted by changes in the time signature. The examples are abundant: I.1, I.2, I.7, II.3, II.9-12, II.28, II.34, II.35, III.1, III.5, III.8, III.9, III.11, IV.2, IV.3 and IV.8.

There are other ways to operationalize irregularities and metric changes without writing a change in the time signature. In exercise II.2, proposed accents (those explicitly indicated by the composer through dynamics symbols), at the beginning of repeated chords, conditions our perception of different time signatures, even though the time signature in the score is 4/4. In exercises II.3 and II.6, the conflict between the meter suggested by the time signatures and the proposed accents is represented by dotted lines. Another way to express new patterns of metric accents is through articulations: in exercise II.22, the standard 2/4, usually divided symmetrically into two groups of four sixteenth, was changed into (3+3+2)/16; in II.26, the accents are a consequence of the harmonic structure. The beaming, however, makes the groupings more explicit and, at times, crosses barlines (such as in I.3, I.6, II.5, II.6, II.14, II.15, II.22, II.25, II.26, II.27, II.39 and III.15). In terms of notation, these operations are interconnected and superposed.

The use of hemiola, an old strategy, but still very much in use today, makes the perception of the meter ambiguous. The term designates a triple rhythmic structure within a binary structure, or the opposite, that is, the ratio 3:2, and its multiples and submultiples in all levels of the rhythmic hierarchy. For instance: two bars with three pulses each can be reorganized, without changing the time signature, into three duple meters (and vice versa); six eighth notes in a compound duple meter (two pulses) can be articulated as three quarter notes in a simple triple meter (and vice versa). There are hemiolas in several exercises - I.3, II.4, II.8, II.25, and II.27. As well, in I.4, the hemiola is used to create changes in tempo between sections.

 

 

Polyrhythm

 

The simultaneity of two conflicting rhythms - polyrhythm - can be observed in exercises I.5, II.51, III.2, III.12, III.13, III.14, III.16, and III.36 up to III.38.

 

 

Polymeter

 

Just like changes in time signatures, polymeter (that is, the simultaneity of two or more meters) can be perceived, even though they have not been explicitly written. Different notational strategies can be used: in short passages or when metric conflicts between levels are not great, each one can be written with a different time signature that express their metric structure; in long passages or in those in which interactions are particularly complex, however, composers prefer using a single time signature for all levels. In this case, polymeter occurs due to accentuation and rhythmic groupings. There are polymetric parts within a single measure in II.5, and in different measures in II.29 and II.30. At times, polymeters, polyrhythms and polytempos are superimposed, such as in exercises II.39 and in III.15.

 

 

Polytempo

 

The idea of polytempois less familiar, but it was also explored in the music of the 20^thcentury: the simultaneity of two or more tempos, whether they are explicitly written or just implied by the metric structure. There are examples of polytempo in the Cartilhain exercises II.29, II.30 and II.39 up to II.41.

 

 

Asynchrony

 

Asynchrony, a gap between plains in any level of the metric hierarchy, is identified in the Cartilha in situations where differences of speed between them may or may not occur.

In exercise II.22, a canon in 2/4, a reference note value (the sixteenth note) is grouped additively (3+3+2) in the two levels of the composition. The melodic movement highlights the rhythmic displacement between them; in II.7, simultaneous groupings with seven units each, although in different speeds, are established: while the right hand performs a group in eighth notes, the left hand performs two in sixteen notes. There is synchronicity at the beginning of each measure; however, in 8.4, a sixteenth note is added to the sixteenth-note group, causing a gap. Until 10.4, the levels are played at the same speed (both in eighth notes), but between 10.5 and 16 they go back to the original difference in speeds and the structure of the left hand (the groups of seven sixteenth notes) is repeated until the original synchronicity is restored. Another example of asynchrony can be observed in exercise II.6.

Often, asynchrony is a result of polymeter, such as in the previously mentioned rhythmic chorales (II.29 and II.30), but can also take place because one metric structure is being played at two different speeds. In exercise II.39, in simple triple meter, the composer overlaps groups of three quarter notes in the left hand and a quicker tuplet structure, quintuplets or septuplets, which are accentuated every three notes. Similar strategies were used in exercises II.40 and II.41. The durations of the superior level are quicker than those of the inferior level, and the result is a simultaneous effect of polymeter, polytempo and asynchrony.

Broadly speaking, polyrhythm, polymeter and polytempo produce more or less complex asynchronies.

 

 

Controlled changes in speed and tempo

 

The Cartilha uses several strategies to address changes in speed. In many, such changes are operationalized through quantitative changes in rhythmic groups, in any level of the metric structure. In exercise II.3, for instance, the effect of a continuous acceleration or deceleration is caused by increasing or decreasing the number of repetitions of an event, without changing the speed of its durations; in exercises II.33 and III.14, the acceleration occurs due to the use of increasingly shorter durations at the inferior level of the metric structure, where an abundant number of tuplet groups were used; meter changes, associated to the successive increase or decrease in the number of reference rhythmic figures at each measure produce a sense of deceleration in exercise III.9 (between measures 2 to 9) and of acceleration in the starting measures of III.10.

Sudden changes in speedwere operationalized through the alternation of long and short notes in whole sections (II.34), through the alteration of the note value (denominator) and the number of beats per measure (numerator) (III.1), or of only the note value (III.8).

Metric modulation- another strategy to control acceleration and deceleration, which frequently involves changing time signatures - is a very particular way of structuring the meter. The term modulation is used because the change is implemented through a pivot duration which, similar to the pivot chord used in harmonic modulation in tonal music, provides a cohesion unity to the movement from one duration to the other. The change in tempo is operationalized very precisely because it evens out a duration or time proportion in the previous tempo to a different duration or time proportion in the following tempo. Proportional tempo changes are not a new idea, but 20^th-century composers have used it more frequently and with greater complexity.

The expression metric modulation has been criticized by a few authors. They argue that the expression suggests that the goal of the process is to change meters, while, in reality, they are agents of tempo changes.The exercises of metric modulation in the Cartilhaare good examples of why this expression is inadequate, because they operationalize controlled tempo changes without modifying the time signature. Maybe that is the reason why Almeida Prado grouped them under the term "rhythmic modulation." This expression, however, is rarely found in the literature dedicated to rhythm in the 20^thcentury.

Exercise II.36 illustrates the strategy above. Written as a 2/4, it consists of a formula (introduced from measures 1 up to 4.1) that is successively transposed to the 12 tones of the chromatic scale. At each transposition, the composer indicates the temporal modulation to be applied - the duration of the eighth note of the triplet determines the duration of the eighth note in the following measure. The modulation is facilitated, however: the first measure has eighth notes in the left hand; in the following measure, the eighth notes are superposed by eighth-note triplets in the right hand; in the third measure, every two of the eighth notes in the triplets are accentuated, making the groups of two eighth notes of the right hand sound faster than the groups of two eighth notes of the left hand, at a 3:2 ratio. From the fourth measure onwards, the speed of the eighth notes in the right hand will be the speed of the eight notes in the left hand. The accentuation, therefore, anticipate the modulation that the pivot note indicates.

The fact that the exercise is harmonically structured into triads allows that all the attention of the performer is dedicated to the rhythm. The difficulties are two. One is the ability to perform the accents within the triplets, since only the first coincides with the downbeat. The other is transforming the new group into a new time unit. However, as the tempo increases with the successive modulations, the execution of the repeated chords becomes increasingly difficult. In the sixth modulation (measure 16), the eighth note reaches an unfeasible metronomic speed - 486 -, forcing the performer to interrupt the transpositions. In exercise II.37, the interruption occurs ahead of the cycle, because the acceleration process is slower. In III.39, on the other hand, the controlled deceleration leads to tempos that are so slow that, in the fifth modulation, no rhythmic relationship can be perceived between the two parts, which also leads to the interruption of the cycle of transpositions.

Generally, performers want to reach the tempos suggested by composers. Sometimes, however, these may not be adequate. This is the case of exercises II.36 and II.37. Despite that, what matters here - as in the Cartilhaas a whole - is the understanding and the performance of the implicit principles.

 

 

Ametric rhythms

 

We recognize the meter of an excerpt by listening to how pulses are divided and grouped. Even when there are changes in time signatures or non-traditional time signatures are used, we are able to identify them - although our capacity to understand metric organization depends on many factors, including whether we know the piece beforehand or not.

Some pieces seem to have a non-perceivable metric organization, called ametric organization. In terms of notation, this effect can be obtained with or without a time signature. Even if there is a time signature, these pieces sound free, as if they are being improvised (III.12, IV.2, IV.3). Exercise III.2 produces the same effect, only without a time signature; but not every piece written without a time signature is ametric. In exercise I.9, a few passages have ametric characteristics, but there are also elements of a metric organization. Usually, if there is no time signature, one rhythmic figure guides the proportionality between the different durations. In III.10, despite the lack of a time signature, the barlines and the form of notation as a whole make it clear that there is a variable metric organization. In his work on theories of rhythm, Smither highlights three musical factors that lead to three different uses of barlines: to indicate points of metric accent in monometric (that is, those in which the time signature does not change), or multimetric pieces; to facilitate the counting of beat units,; or in pieces with explicitly omitted time signatures (whenever measures with unequal durations are used), to indicate note groupings.

The written meter is more a frame for the metric structure than an actual description. Performers should not assume that only the notation would provide them with the means to understand the metric structure of a piece. Beyond notation, it is the phenomenological result of the relation between all elements of musical discourse, in all levels of the metric hierarchy, that should guide rhythmic analyses.

Often, the motivation to find new rhythmic strategies emerges from studies in non-Western musical traditions. To mention only two very representative composers: Olivier Messiaen (1908, 1992) finds elements from Hindu music and the metrics of ancient Greek music, and Béla Bartók (1881, 1945) uses East European folk music. Having studied with Messiaen, it is only natural that Almeida Prado uses a few strategies explored by the French composer in his groups of exercises based on Greek and Hindu rhythms. 

African rhythms are also addressed.

 

 

Greek rhythms

 

According to Maurice Emmanuel, the Greeks did not separate music from poetry, dance and dramatic arts. Their understanding of rhythm was based on a small unit - primary time (chronos protos) -, which they considered a minimum, indivisible duration applicable to sound, syllables and movements of the body. In Greek poetry, syllables have two different possible durations: short (U), which corresponds to the chronos protos, and long (-), that is, twice as long.

The groups of shorts and longs were called feet, a term still used today in the study of rhythm. The most important among the triple meters - with three chronos protos- are the "iambic" - formed by the succession of one short and one long (U -) - and the "trochee" (or "choree") - formed by a long and a short  (- U). Among the quadruples, with four chronos protos, there is the "spondee", formed by two longs (- -), the "dactyl, by one long and two shorts (- U U), the "anapest", by two shorts and one long (U U -) and the "amphibrach", by one long between two shorts (U - U). Among the quintuple, with five chronos protos, there is the "cretic", which includes a succession of one long, one short and one long (- U -), and the "bacchius", with one short and two longs (U - -). Among the composed feet, there is the "choriambic," a trochee alternating with an iambic, that is, one long, two shorts and one long (- U U -).

The Greek principles of rhythm were fundamentally different from "ours," because they used a small unit, which they considered indivisible (additive principle), whereas we break our units, the whole note, into two or three parts (divisive principle), the only limitation being the possibility to perform such speeds.

In the Cartilha, Almeida Prado uses the Greek feet in unusual metric structures, associating them, in a canon, to the Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Lochrian and Ionian modes (II.14 to II.20).

 

 

Hindu rhythms (III.17 to III.31)

 

According to Messiaen, the Gandharva Veda-the Vedaof celestial musicians - recognizes the existence of four music systems in India, which are associated with the gods Shiva, Soma, Hanuman and Bharata. Supposedly, it was Shivathat taught music and dance to people, six thousand years before our era. Shiva'ssystem includes ten different modes, all of them pentaphonic. The modes in the Carnatic system of Southern India, associated to Soma, are all heptaphonic. When all possible alterations are applied to all its degrees, except over the first and the fifth, it creates 72 different modes that can be split into two classes, according to their fourth degree: in the 36 modes of the çaddha-madhyamaclass, the interval between the fourth degree and the tonic is perfect; in the 36 of the prati-madhyama class, it is augmented.

Messiaen uses the word tala with its first and most important meaning, that is, rhythm, but also in a sense of rhythmic pattern. He then introduces the seven talas in the Carnatic theory - dhruva, mátsya, rúpaka, jhampa, triputa, atatâla andekatâla- and its five subtypes - tíshra, chaturúshra, cúndh, míshra e sankírna. The following table introduces the 35 rhythmic possibilities in the theory. It is possible to write them in traditional western notation, for instance, if we consider an eighth note as equal to the number 2. In this case, the dhruva-tishratala (exercise III.17) was translated as the succession of a dotted eighth note, an eighth note and two dotted eighth notes.

 

 

subtype tala	Tíshra	Chaturúshra	Cúndh	Míshra	Sankirna
Dhruva	3-2-3-3	4-2-4-4	5-2-5-5	7-2-7-7	9-2-9-9
Mátsya	3-2-3	4-2-4	5-2-5	7-2-7	9-2-9
Rúpaka	3-2	4-2	5-2	7-2	9-2
Jhampa	3-1-2	4-1-2	5-1-2	7-1-2	9-1-2
Triputa	3-2-2	4-2-2	5-2-2	7-2-2	9-2-2
Atatâla	3-3-2-2	4-4-2-2	5-5-2-2	7-7-2-2	9-9-2-2
Ekatâla	3	4	5	7	9

 

 

Messiaen also describes the 120 deci-talas - popular talas - of the Çârngadeva system. These can be found in the fifth of the seven books of the Samgîta-ratnâkara, written in Sanskrit in the 13^thcentury, the musical diamond mine. The book focuses on three talas: parvatilocana, sarasvatikanthabharanaand lakskmiça.

In Hindu theology, each deity is accompanied by his wife - or, more precisely, by his feminine aspect, of manifestation power, of its Shakti. Therefore, Parvati is Shiva's Shakti, Lakshmi is Vishnu's and Sarasvati is Brahma's.

Parvatilocanameans "Parvati's eyes." This tala is represented as follows, in Western notation:

 

 

 

Lakskmiçameans "calm like the peace that comes from Lakskmi," the goddess of fortune and beauty, represented by four lines, just like Vishnu, which explains the four durations of the tala:

 

 

 

Sarasvatikanthabharana means Sarasvati's necklace. Sarasvati is the goddess of words, science and the arts (especially music). The tala represents a progressive acceleration - increasingly shorter durations, always in pairs - as opposed to the progressive rallentandoin durations of the tala lakskmiça:

 

 

 

In exercise III.17, Almeida Prado gathers the rhythmic elements of the talas in the Carnatic theory with the notes of the ten pentaphonic modes in Shiva's system. In III.18, Prado combines modes 46 and 68 of the prati-madhyamaclass. The combination of the three talas of the Çârngadeva system and mode 50 of the prati-madhyamaclass produced 13 exercises (from III.19 to III.31). The additive principle is prevalent in all of them. In some (III.21, III.22 and III.28), however, Prado does not follow the reference Hindu tala rigorously.

 

 

African rhythms

 

In exercise I.8, Almeida Prado uses a rhythmic pattern common in African music, designated as timeline, a temporal reference by which the phrase structure of a song as well as the linear metrical organization of phrases are guided. The timeline pattern is usually clapped or played by any instrument with a penetrating sound, such as a bell – hence the term "bell-pattern" - , in an ostinatoof 12 or 16 asymmetrically-organized units (5+7 or 7+9, for instance), together with the melody or the rhythm played by the other musicians. Singers, percussionists and dancers find support in the beats of the timeline, which is repeated throughout the performance.

To prepare students for more difficult exercises, Prado introduces timeline variations with 12 units, similar to those in exercise I.8, to be performed only rhythmically.

 

 

A few Brazilian rhythms

 

At the end of Volume II, the exercises grouped under the title A few Brazilian rhythmsillustrate the syncretism of elements from European, African and Indigenous cultures, all of which contributed to the variety and diversity of Brazilian music. Throughout this suite, performers will be presented with sonorities akin to music styles such as maracatu, caboclinhos,coco, frevo, baião, samba, as well as the striking of the atabaques(a Brazilian hand drum), played in ostinato. The syncopations in the score often hide additive rhythms that coexist with the simple duple meter (or its direct derivations).

 

There are still a few exercises whose goal is not to address specific rhythmic issues, but to illustrate ways to compose, such, for instance, 12-tone-serialism (II.24). The three last exercises in the Cartilhaare based on ideas put forth by Almeida Prado in the exercises: peregrine harmony (IV.8), serial dodecaphonic serialism mode (IV.9) and diatonized dodecaphonic serialism (IV.10).

 

 

Brief analysis of the exercises

 

Volume I: 11 exercises

 

I.1 Changes in meter.Ciranda

Alternation between a constant 4/4 (8/8) pattern and a pattern that progresses additively, from two (2/8) to 13 (13/8), both inspired by the melodic design of the first exercises in Czerny's book (C-D-E-F-G-F-E-D-C). Alternation between major triads and major minor-seventh chords in accompaniment. Metric change always indicated by changes in the time signature.

 

I.2 Different articulations. After J. S. Bach's prelude in C minor, BWV 999

A dialogue between a motif based on J. S. Bach's Prelude in C minor, BWV 999, and its transformations, put forth through indirect derivative time signatures and harmonic/melodic interferences. Like the previous exercise, metric changes always indicated by changes in time signatures.

 

I.3 Different accentuations in 6/8.Catira

Accents and articulations (2+2+2, 3+2, 3+2+3, 3+4, 3+3+3+4, 4+5) that clash with the meter established by the rhythm in the compound duple meter of the Catira. Emphasis upon the hemiola at the beginning of the exercise: two compound beats followed by three simple beats, without changing in time signature. Coexistence of 6/8 meter with metric changes indicated by dashed lines and different time signatures written above the score.

 

I.4 Waltz in four tempos. Dreams in lilac

Changes in tempo and time signature operationalized through hemiolas in the triple meter of the waltz.

 

I.5 Rhythmic Tango.Corrientes579

Flexibilization, by way of syncopations, tuplets and polyrhythms, of the regularity and rigidity of the simple quadruple meter suggested by the chords played in a rhythmic ostinatowith the left hand, with a shifted accentuation in the fourth beat, typical of the Argentinean tango. Reference in the title to "Corrientes 349, segundo piso ascensor, no hay porteros ni vecinos..." ["Corrientes 349, on the second floor, there are no doormen or neighbors..."] a famous tango sung by many generations in honor of Corrientes Avenue, a landmark in the Buenos Aires cultural scene of the 1930s.

 

I.6 Various accentuations in 2/4.Chorinho

Interferences through accents and conflicting articulations in the metric established by the rhythm in simple duple meter, characteristic of chorinho. Like in the Catira(I.3), coexistence of the 2/4 with metric changes indicated by dashed lines and different time signatures added above the score.

 

I.7 Alternated articulations

Alternation between one chord and a succession of major seconds articulated in larger or smaller groups indicated by successive changes in time signature. Beginning of each group marked by an accentuated chord.

 

I.8 Various articulations and accents in 12/8

Use of a timeline (see note 31) of 12 units with some rhythmic variations: 7+5, 5+7 (7=2+3+2 or 3+2+2 or 2+2+3 and 5=2+3 or 3+2) or even 2+2+2+2+2+2.

 

I.9 Various figures and accents with resonances.Ad laudes matutinas

Laudes,first collective prayer of the day. Inspired by the monastic liturgy of the Benedictines. Stylization of the plainsong, by means of repeated notes, abundant number of tuplets of various numbers of elements and polyrhythms. Antinomy between the duration of the minimum reference, the 32^ndnote, and the random durations of the resonances - dependent on the acoustics of the instrument and of the concert hall -, producing an ametric effect. Reference figure grouped in longer units (quarter notes), without establishing metric accents. Piece with five sections, each predominantly using a certain register of the instrument. Three possibilities for ordering the sections, always maintaining the first and last sections at the beginning and at the end of the piece. Two complementary rhythmic systems in the performance: additive and divisive, such as, for instance, in section E.

 

I.10 Quintuplets and septuplets in 2/4. Nocturne

Regularity in the melody in a simple duple meter flexibilized by an accompaniment ostinatofigure in quintuplets in chopinian stile.

 

I.11 Various articulations with growing intervals. Spinning top

Rhythmic-melodic groupings of variable extension, indicated by frequent changes of time signature, formed by a succession, in opposite movement, of chromatically growing intervals, from a semitone to an octave. Random number of repetitions of the groupings.

 

 

Volume II: 51 exercises

 

II.1 to II.8 Fixed pulse

Fixed pulse from the beginning to the end of each exercise. Meter changes determined by proposed accents, as well as harmonic and melodic elements and articulations, without changing the time signature (except for II.3).

 

II.1 Fixed pulse with varied accents over a pivot major triad

Fixed pulse in the left hand, established by an uninterrupted number of C major triads, always with the same speed, superimposed to a chromatic sequence of major triads, played in unpredictable moments and registers.

 

II.2 Fixed pulse with varied accents

Chords with three or four notes, articulated uninterruptedly, alternating the hands. Meter disturbed by proposed accents.

 

II.3 Fixed pulse with decreasing and increasing durations

A decreasing and then increasing number of groups (from 12 to 1 and back) formed by a rhythmic pattern uninterruptedly repeated in both hands, in contrary motion. Meter changes - followed by a chromatic displacement in the pattern - always indicated by time signatures.

 

II.4 Fixed pulse of three eighth notes with articulations of three 16^thnotes

Superimposed meters written in the same time signature (3/8). Polymeter as the result of two groups of three 16^thnotes (6/16) in the upper staff, and three 8^thnotes (3/8) in ostinato, in the lower one. Synchrony between the two meters. A good exercise for practicing hemiolas (the 3:2 ratio): six 16^thnotes in the right hand, arranged in two groups of three 16^thnotes, and six 16^thnotes in the left hand, arranged in three groups of two 16^thnotes, coagulated into 8^thnotes.

 

II.5 Fixed pulse of four 8^thnotes with articulations of four and three 16^thnotes

Variable meter superimposed on a fixed meter, both written in the same time signature (4/8). Polymeter as the result of the succession of two inequal groups of 16^thnotes (4+3), in the upper staff, and two groups of two 8^thnotes in ostinato derived fromthe same melodic/harmonic elements of the ostinatoof the previous exercise, in the lower one. Synchrony and asynchrony between the levels. 

 

II.6 Fixed pulse of five 8^thnotes with articulations of five 16^thnotes

Superimposed meters written with the same time signature (5/8). Polymeter as the result of the superimposition of two groups of five 16^thnotes, in the upper staff, and two groups (one with three and the other with two 8^thnotes) in ostinato derived fromthe same melodic/harmonic elements of the ostinato of the previous exercise, in the lower one. Asynchrony between the two meters starting at measure 8. 

 

II.7 Fixed pulse of seven 8^thnotes with articulations of seven 16^thnotes

Superimposed meters written with the same time signature (7/8). Polymeter as the result of the superimposition of three groups of 8^thnotes (3+2+2) in ostinato derived froma transposition of the melodic/harmonic elements of the ostinatoof the previous exercise, in the upper staff, and two groups of seven 16^thnotes in the lower one. Asynchrony after measure 8.4. 

 

II.8 Fixed pulse with nine 8^thnotes with articulations of nine 16^thnotes

Superimposed meters written with the same time signature (9/8). Polymeter as the result of the superimposition of two groups of nine 16^thnotes, in the upper staff, and three groups of three 8^thnotes in ostinatoderived from a transposition of the melodic/harmonic elements of the ostinatofound in the previous exercise, in the lower one. Synchrony between the two meters. A good exercise for practicing hemiola (the 3:2 ratio): 18 16^thnotes in the right hand, arranged in two groups of nine 16^thnotes, and 18 16^thnotes in the left hand, arranged in three groups of six 16^thnotes, coagulated into 8^thnotes. 

 

II.9 to II.12 Common denominator

Exercises with frequent changes in time signature. Variations in both the numerators and the denominators. Common denominator established by the shortest note of all time signatures, in each exercise. For instance, in exercise II.10, 8^thnote as common denominator for 4/4, 3/4, 5/8, 2/4, 7/8, 5/4, 9/8, 11/8, 4/8, 3/8 and 6/4.

 

II.13 and II.14 Scales in a canon

Different scales - major/minor diatonic, Greek modes, enigmatic, oriental, overtone, serial - in canons, with variable rhythmic displacement between the two entries of the piece, as well as different intervals between them.

 

II.13 Diatonic scales. Major and minor scales in canon at the fifteenth

Canon alla15^ma, the second voice starting one full measure from the other. Single rhythmic pattern in a fixed simple duple meter (2/4) with syncopations applied to diatonic scales, major and minor (harmonic, melodic and modal) and Neapolitan (major and minor), in all keys. Frequent incidence of the tonic in the weak beat or weak part of the beat, and asynchrony of its occurrence between the hands.

 

II.14 to II.20 Greek modal scales

Different additive rhythmic patterns with a variable number of chronos protos,inspired by the feet in Greek poetry metrics, applied to the seven modal diatonic scales. Conflict between the lower and upper voices of the canon produced by the superimposition of different feet.

 

II.21 Unusual scales I. Enigmatic mode. Canon at the octave and accents forming a scale

Exercise with a formation law determined by the distribution of the seven notes in the enigmatic scale in one longer figure (8^thnote) and six shorter (16^thnotes), organized divisively in a duple meter (2/4). In each repetition of the scale (ascending for the first three repetitions and descending for the rest), shift of the position of the 8^thnote - and, consequently, of accent – to the second division of the measure, and successively to the third, fourth, fifth and sixth divisions of the following measures. Canon at the octave, the inferior part shifted one quarter note.

 

II.22 Unusual scales II. Oriental mode. Groups of intervals in canon at the tenth with 3+2+2 articulations

Oriental scale combined with rhythmic pattern of 16 isochronous units grouped in sets of two (3+3+2) and distributed in two simple duple meters (2/4). Transposition of the model to each degree of the scale. Gap between the structures created by the beginning of the inferior part a dotted 8^thnote after, in the sixth degree, in a canon at the tenth.

II.23 Unusual scales III. Overtone scale. Resonance of superior harmonics and canon at the eleventh

First seven distinct tones of the overtone series played in succession, followed by a canon at the eleventhon the overtone scale in a simple quadruple meter. Sustain pedal activated throughout the entire exercise. Resonance of the superior harmonics highlighted at the end with an accent on the successive degrees of the mode, placed on the dotted notes.

 

II.24. Unusual scales IV. Serial mode, canon at the twelfth

Series of twelve different sounds formed by two identical tetrachords (Dorian) separated by a half step, followed by four notes in minor-third intervals. Canon at the twelfth below starting two beats apart in a simple quadruple meter.

 

II.25 to II.28 Accent Variations
Exercises with multimeters and polymeters without changes in time signatures. Metric regularity altered by articulations, proposed accents and variations in the extension of the harmonic/melodic structures, combined differently in each of the exercises. Beaming across barlines.

 

II 25. Accent variation in 6/8

Similar to exercise II.24, 12 notes are distributed into four triads, two of them major and two of them minor. Rhythmic/melodic groupings typical of compound duple meters and formed by those triads played in chords or arpeggios. Superimposition of different groupings with the same number of elements or a variable number of elements - produced by adding or suppressing notes in the arpeggios of the triads. Metric conflicts and asynchronies highlighted by the accents strategically placed at the beginning of the groups. Frequent use of hemiolas.

 

II.26 Accent variations in 8/8

Alternation between moments of regularity and irregularity. Unpredictable accents due to the varying duration of groups formed by a succession of arpeggiateddominant chords in a pre-established order and position. Emphasis on the beginning of each group both by the repetition of the bass note and by chromatic progression. 

 

II.27 Accent variations in 12/8

Succession of broken altered major seventh chords in a pre-established order and position. Rhythmic groupings as a result of the repetition of the structures and proposed accents conflicting with the regularity of the ternary groupings of the 12/8 meter. 

 

II.28 to II.35 Eight small rhythmic chorales

A study of changes in tempo and polytempo. Various oppositions: forte/piano; vertical/horizontal; fixed tempo (measured)/free tempo (recitative); fixed/moving; long/short and slow/fast.

 

II.28 Changes in tempo with the same pulse in three voices

Meter changes using a constant rhythmic figure (the 8^thnote) as reference. Effect of a change in tempo obtained by stretching or shortening the metric unit.

 

II.29 Two different, simultaneous tempi

Simultaneity of two time signatures, with a constant rhythmic figure (the 8^thnote) as reference in a polyphonic texture, in three voices. Intermediary voice in a different time signature than the top and bottom voices. 

 

II.30 Three different, simultaneous tempi in three voices

Three simultaneous time signatures, with a constant rhythmic figure (the 8^thnote)as  reference in a polyphonic texture, in three voices. Effect of polytempo due to the different rhythmic patterns used for each voice.

 

 

II.31 Two simultaneous tempi with tuplets in three voices

Effect of change in speed caused by quantitative changes in tuplet groupings (from triplets to quintuplets and vice versa). Polytemporal effect produced by polyrhythms.

 

II.32 Dialogue between a fixed or measured tempo and a free (recitative) tempo in four voices

Changes in speed and tempo caused by an alternation between long (in simple quadruple meters) and short notes (in prosodic, additive rhythms).

 

II.33 Slow, accelerating tempo in four voices

Progressive increase, at each measure, of the number of articulations, causing an effect of acceleration.

 

II.34 Tonal-chromatic harmonic sequences in five voices. Half notes with interference of moving 16^thnotes

Acceleration and deceleration controlled by a minimum, common rhythmic figure of reference, the 16^thnote. Increase of one unity in the number of fast articulations every time the moving group intervenes. 

 

II.35 Atonal harmonic sequence in five voices. Moving 8^thnotes and a fixed whole note

Alternation between a long, fixed figure, the whole note, and a variable number of 8^thnotes grouped additively.

 

II.36 to II.41. Tuplets

Use of tuplets - element of cohesion of this set of exercises - operationalizing progressive tempo changes (II.36 to II.38) and the simultaneity of different speeds (II.39 to 41).

 

II.36 Rhythmic modulation I. Progressive acceleration by way of the tuplet 3:2

Controlled acceleration of the tempo by way of a pivot rhythmic figure, an 8^thnote triplet. Chromatic transposition of a model of four measures.

 

II.37 Rhythmic modulation II. Progressive acceleration by way of the tuplet 5:4

Controlled acceleration of the tempo by way of a pivot rhythmic figure, an 8^thnote quintuplet. Chromatic transposition of a model of four measures. 

 

II.38 Rhythmic modulation III. Progressive rallentando by way of the tuplet 3:4

Controlled deceleration of the tempo by way of a pivot rhythmic figure, an 8^thnote triplet. Chromatic transposition of a model of three measures.

 

II.39 Waltz with two triple-meter articulations by way of 8^thnote quintuplets and septuplets

In a simple triple meter, superposition of 8^thnote quintuplets (and later septuplets) in the right hand, accented in groups of three, and quarter notes in the left hand, resulting in two different triple rhythms in different tempos (polytemporality). Acceleration in the superior level of the waltz during the transformation of the quintuplets into septuplets.

 

II.40 March with two duple articulations by way of quarter-note triplets

In a simple duple meter, superimposition of a succession of quarter-note triplets in the right hand, every two of them accentuated, and a pedal chord in quarter note in the left hand resulting in two simultaneous simple duple rhythms in different tempos (polytemporality). Parody of Gottschalk's Variations on the Brazilian Anthem.

 

II.41 Rhythmic pedal of five beats and harmonic progression in quarter-note triplets but articulated every five of them

In a quadruple meter, superposition of a succession of quarter note triplets in the right hand, every five of them accentuated, and a pedal chord in quarter note (every five of them accentuated) in the left hand, resulting in two simultaneous quintuple rhythms in different tempos (polytempos). Quarter note triplets grouped into a 3+2 pattern by way of articulations matching the harmonic progression.

 

II.42 to II.51 A few Brazilian rhythms

Exercises with rhythmic characteristics of Brazilian genres: duple and quadruple simple meters, syncopations, off-beats, shifted accents and tuplets. Polyrhythms, polymeters and asynchrony.

 

II.42 Maracatus of Recife I. A few rhythmic articulations of the gongué and the tarol

Reproduction of rhythmic articulations and sonorities of two instruments used in maracatu: the gongué  (a type of cow bell) and the tarol(a type of snare drum).

 

II.43 Maracatus of Recife II. The rhythmic patterns of Maracatu

Superimposition of articulations of the gongué and the tarol.

 

II.44 and II.45 Caboclinhos I and II

Two instrumental melodies alluding to instruments used in the caboclinhos of Recife: the pífano(a type of small flute) and the caxixi(a type of small rattle).

 

II.46 and II.47 Two African-Brazilian rhythms

African-Brazilian melody superposing a percussive ostinatoin the low register of the piano. Significant use of syncopations.

 

II.48 Coco-de-embolada

Melody with a prosodic rhythm suggesting the coco-de-emboladagenre song, accompanied by a rhythmic/melodic ostinato. Between every variation in the melody, disruption of the regularity by a connecting element based on the ostinato,metrically conflicting with it. Polymeter starting on measure 25 resulting of the superimposition of the melody (in 2/4) over the connecting element (in 3/8).

 

II.49 Frevo

Sections characterized by changes in texture/orchestration alluding to brass ensembles. Frevo'stypical destabilizations, caused by syncopations, off-beats and accents, highlighted by the fast tempo.

 

II.50 Baião

Superimposition of 16^thnotes accentuated in the strong beats and the strong part of the beats in the right hand, to the characteristic baiãorhythm in the left hand. Asynchrony from measure 11 to 14 created by interpolation of five groups (2+3) of 16^thnotes, followed by a group of (3+4).

 

II.51 Batucada. The celebration of all rhythms

Combination of various rhythmic strategies explored in the "A few Brazilian rhythms" group of exercises: rhythmic shifts caused by off-beats and syncopations, proposed accents, articulations and many types of tuplets (producing meter changes) over regular pulses or any event previously mentioned. Complex polyrhythms (12:11, 12:13, 20:17) and controlled acceleration (from four to five, six, seven and nine divisions per measure). Reproduction of rhythmic articulations and sonorities played by the samba school percussion section.

 

 

Volume III: 31 exercises

 

III.1 Rhythmic permutation

Permutation of the order of a series of 12 measures, each one with its own meter. Perception of meter changes facilitated by the pedal note E and minor chord changes. Constant sense of changes in speed.

 

III.2 Interval and rhythmic spatialization

Sense of obscured pulse achieved through the dispersion of intervals and durations in contrasting registers.

 

III.3 Two simple simultaneous tuplets

Superimposition of a quintuplet and a triplet. Transposition of the two first measures following a whole-note scale. As exercise I.1, inspired by Czerny,

 

III.4 Sudden change in the articulation in a diatonic progression

Organization of a 5/8 time signature into a 4/8 + 1/8. Contrast between the 4/8 — 8^thnotes in ascending motion – and the 1/8 - 32^ndnotes in descending motion. Transposition of the model established in the first measure following the C major scale. Also inspired by Czerny.

 

III.5 Variety of speeds

Meter changes written through variation in time signatures, many with unusual numerators (13, 17, 19, 20) and denominators consecutively varying from long to short figures, and vice-versa, causing variations of speed.

 

III.6 Upbeats

Ambiguity between the written form and the perception of the upbeat, clarified by the articulation of the accentuated chord on the downbeat. 

 

III.7 Syncopations and tuplets

Rubatoeffect produced by subtle differences between rigorously written syncopated and tuplet rhythms. Near the end, controlled acceleration produced by increasingly shorter durations.

 

III.8 Changes in pulses: three, four and five

Exercise with three sections in different meters - triple, quadruple and quintuple -, played in three-note chords. Acceleration and deceleration in each section, depending on the denominator used.

 

III.9 Time signature changes around a pivot note (F^#, G, A^b, A, A^#)

Successive meter changes associated to broken chords, with the 8^thnote as reference, after an introduction in 32^ndnotes. Perception of the two, three and four 8^thnote groupings facilitated by a pivot note (pedal). Metric changes operationalized by way of harmonic changes. At a fast speed, perception of two different beat units - a quarter note and a dotted quarter note - within one measure. Controlled deceleration between measures two and nine due to meter changes associated with the increasingly greater number of reference rhythmic figures each subsequent measure.

 

 

III.10 Reducing and increasing durations around a pivot note (E)

Constant rhythmic figure of reference (16^thnote). Up to the 19^thmeasure, controlled acceleration caused by elimination, at every measure, of the last of a series initially presented with 19 notes, always ending at the accentuated pivot note. Repetition of the pivot note at measure 20. Next, sequences with a variable number of articulations and melodic contours, always ending at the pivot note. Perception of meter changes although without written time signature.

 

III.11 Interrupted minimalism

Repeated measures with unusual numerators (13, then 16, 19 and 23 beat units), organized in irregular groupings of three and two 8^thnotes. Repetition interrupted by contrasting ideas in terms of duration, tempo, rhythmic figures, range and dynamics. Minimalism characterized by economy of material and by repetition. Exercise extremely dense and diversified, despite the title.

 

III.12 Continuous quintuplets

Continuous 8^thnote quintuplets over and under continuous 8^thnote triplets, eventually interrupted by groups of four 8^thnotes or variations. Duple meter indicated by the composer obscured by polyrhythms.

III.13 Simultaneous tuplets

Use of minimalism. Three sections, formed by five continuous groups of 16^thnote sextuplets over five groups of 16^thnote quintuplets, repeated seven times. Permutation and variation of the notes in the groupings. Subtle variations from one section to the other.

 

III.14 Variety of tuplets

Succession of tuplets with a growing number of elements over, and then under, a pattern of four 8^thnotes. Alternation between one hand and the other, at the end, of a pattern of three against two.

 

III.15 Tuplets with pauses in 2/4

Tuplets in the right hand with a varied number of elements and pauses over a regular background of quarter notes, in the bass section, and 8^thnotes articulated every two in the middle range, in the left hand. Asynchrony between metric accent and accents in the tuplet groupings.

 

III.16 Tuplets with pauses in 4/4

A succession, in both hands, of tuplet groupings with a varied number of elements (3, 5 and 7), started and interspersed by pauses, without occurrence of superposition of groups with the same number of elements.

 

III.17 to III.31 Hindu rhythms

Three groups of exercises. In the first, ten different rhythmic talas in the Carnatic system combined with ten pentatonic modes in Shiva's system, superimposed to a resonant chord formed by notes of the mode. In the second group, two rhythmic talas in the Carnatic system combined with two Prati Madhyama heptatonic modes, also superimposed to a resonant chord formed by notes of the mode. In the third group, fourteen exercises freely composed, based on the combination of another Prati Madhyama mode combined with three rhythmic talas in the Çarngadevasystem: parvatilocane, sarasvatikanthabharanaand lakskmiça.

 

 

Volume IV: 10 exercises

 

IV.1 Multiple articulations I

Supertuplets, repeated notes, off-beats and syncopations. Prevalence of septuplets. New texture at measures 8, 13-15 and 45-46 in pp,like a cloud of sounds.

 

 

 

IV.2 Multiple articulations II

Chords, one at each measure, in ffand at varied registers. Effect of ametric rhythm caused by a frequent change in time signatures. Interruption in the flow of chords by the overtones of the minor seventh interval G-F. Biphonic, polyrhythmic texture in 4/4, with shorter durations, played in pppover that interval. Return of the chords at measure 14.

 

IV.3 Multiple articulations III

Fifth variation of Ta'aroa(1971), with measures 19, 20 and 21 rhythmically varied. Piece inspired by the Tahitian cosmogonic myth and the name of the Polynesian two-faced goddess. Exercise developed in two levels: a series of 12 sounds - E^b(D^#), A^b(G^#), B^b(A^#), B, E, D, A, C, G, C^#, F, F^#- in longer durations, repeated backwards a half-step above, in the first level; in the second one, alternation between repeated notes, organized in groups with a varied number of elements, and segments in two voices. Complex rhythmic counterpoint between the voices produced by the superimposition of groupings with conflicting articulations and number of elements. Emphasis on quintuplets with interspersed pauses. Piece not submitted to the dodecaphonic technique despite the use of a series and its retrograde.

 

IV.4 to IV.7 Playing with rhythms with regular and irregular articulations

Subdivision of the metric unity into isochronous durations (16^thnotes) grouped into two superimposed, different patterns: the superior, consonant with the meter; and the inferior, dissonant. Polyrhythms in the metric level. 

 

                                                          3x 4 16^thnotes + 4 16^thnotes

IV.4.    16 16^thnotes =            ----------------------- --------------

                                                          4 x 3 16^thnotes    + 4 16^thnotes 

 

                                                          5 x 4 16^thnotes   

IV.5.    20 16^thnotes =            -------------------

                                                          4 x 5 16^thnotes    

 

                                                          7 x 4 16^thnotes   

IV.6.    28 16^thnotes =            --------------------------         

                                                          4 x (3 + 4 ) 16^thnotes  

 

 

                                                          11 x 4 16^thnotes   

IV.7     44 16^thnotes =            -----------------------------------------------           

                                                          2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 16^thnotes   

 

IV.8 Rhythmic passacaglia/chaconne

Seven variations over a sequence of altered chords (peregrine harmony) of different durations. Rhythmic issue expressed in the subtitles, at each variation: spatialized syncopations;repeated 8^thnotes with varied accents in octaves; continuous 8^thnotes in octaves within each measure; G pedal in 8^thnotes and irregular interval interventions; tuplets: one extra beat in each measure; irregular tuplets; harmonic anticipations by means of appoggiaturas.

 

IV.9 Metric alternation. Rhythmic chorale

Rhythmic choral illustrating the serial dodecaphonic mode. Alternation of time signatures without changing pulses or speeds.

 

IV.10 Metric alternation. Diatonized rhythmic chorale

Diatonization (in E major) of the rhythmic chorale in the previous exercise.

 

 

References

 

 

Works cited

 

AGAWU, Kofi. Representing African music. Postcolonial notes, Queries, Positions. New York: Routledge, 2003.

 

ANDRADE, Mario. Dicionário Musical Brasileiro. São Paulo: Editora da Universidade de S. Paulo e Editora Itatiaia, 1989.

 

APEL, Willi. Harvard Dictionary of Music. Second edition. Cambridge: the Belknap Press of Harvard University Press, 1972, p. 165.

 

AROM, Simha.Polyphonies et polyrythmies instrumentales d’Afrique Centrale. Paris: SELAF, 1985.

 

BERNARD, Jonathan. The evolution of Elliott Carter’s rhythmic practice. Perspectives of New Music,1988: 164-203.

 

CASCUDO, Câmara. Dicionário do Folclore Brasileiro.Rio de Janeiro: Instituto Nacional do Livro. 1962.

 

EMMANUEL, Maurice. Histoire de la langue musicale. Paris: Librairie Renouard, 1908, vol. I.

 

GANDELMAN, Salomea. 36 compositores brasileiros: obras para piano (1950/1988).Rio de Janeiro: Funarte/Relume-Dumará, 1997.

 

KOELLREUTTER, Hans J. Terminologia de uma nova estética da música.Porto Alegre: Movimento, 1990, 2^aedição. 

 

LAVIGNAC, Albert. Encyclopédie de la musique et Dictionnaire du conservatoire. Paris: Librairie Ch. Delagrave, 1913, parte I.

 

SACHS, Curt. Rhythm and tempo. A study in music history.New York: W.W. Norton & Company, 1953.

 

MESSIAEN, Olivier. Traité de rythme, de couleur, et d’ornithologie.Paris: Alphonse Leduc, 1949-1992, vol. I.

 

PERSICHETTI, Vincent. Twentieth-century harmony: creative aspects and practice. New York: Norton, 1961.

 

SCLIAR, Esther. Elementos de teoria musical.São Paulo: Novas Metas, 1986.

 

SIMMS, Brian R. Music of the twentieth century.New York: Schirmer Books, 1986.

 

SMITHER, Howard. Theory of rhythm in the nineteenth and twentieth centuries with a contribution to the theory of rhythm for the study of twentieth-century music. Doctoral Dissertation. Cornell University, 1960.

 

SWANWICK, Keith. Music, mind and education(1988).London and New York: Routledge, 1994.

 

______.Musical knowledge.London and New York: Routledge, 1994.

 

SWANWICK, Keith and TILLMAN, June. The sequence of musical development.In:British Journal of Music Education, v.3, no. 3, 1986, p. 305-339.

 

WINOLD, Allen. Rhythm in twentieth-century music. In: DELONE, Richard et al. Aspects of twentieth-century music. New Jersey: Prentice-Hall, 1975.

 

 

Scores

 

ALMEIDA PRADO. Jose Antonio de. Cartilha rítmica para piano. Campinas. Author’s original manuscripts , 4 vols., 1992-2005.

 

 

Doctoral Dissertations on Almeida Prado and his work for the piano

 

ALBRECHT, Cintia Costa Macedo. Um estudo analítico das sonatinas para piano solo de Almeida Prado visando a sua performance. Tese de Doutoramento. Universidade Estadual de Campinas (UNICAMP), 2006.

 

ALMEIDA PRADO, José A. de. Cartas Celestes, uma uranografia sonora geradora de novos processos composicionais.Tese de Doutoramento. Universidade Estadual de Campinas, 1985.

 

CORVISIER, Fernando. The ten piano sonatas of Almeida Prado – the development of his composicional style. Doctoral Dissertation. University of Houston, 1997.

 

GOMES FILHO, Tarcísio. A prática intertextual em peças para piano de Almeida Prado: elementos de análise para construção da performance. Tese de Doutoramento. Universidade Estadual de Campinas (UNICAMP), 2010.

 

 

Master Thesis on Almeida Prado and his work for the piano

 

ASSIS, Ana C. de. O timbre em Ilhas e Savanas, de Almeida Prado – uma contribuição às práticas interpretativas.Dissertação de Mestrado. Universidade Federal do Estado do Rio de Janeiro, 1997.

 

BENETTIJunior, Alfonso. Comunicação estrutural e comunicação emocional nas Variações sobre um tema nordestino de Almeida Prado. Dissertação de Mestrado. Universidade Federal do Rio Grande do Sul, 2008.

 

COSTA, Régis G. da. Os momentos de Almeida Prado: laboratório de experimentos composicionais.Dissertação de Mestrado. Universidade Federal do Rio Grande do Sul, 1998.

 

COSTA, Thiago de Freitas Câmara A edição crítica e revisada dos noturnos para piano de Almeida Prado.Dissertação de Mestrado. Escola de Comunicações e Artes/USP, 2011.

 

FONTANA, Tauir Agnoletto. Decisões interpretativas nas Cartas Celestes I de Almeida Prado.Dissertação de Mestrado. Universidade Federal do Rio Grande do Sul, 2012.

 

FRAGA, Elisa M. Zein. O livro das duas meninas, de Almeida Prado: uma outra leitura.Dissertação de Mestrado. Universidade Estadual de Campinas, 1994.

 

GROSSO, Hideraldo L. Os prelúdios para piano, de Almeida Prado – fundamentos para uma interpretação.Dissertação de Mestrado. Universidade Federal do Rio Grande do Sul, 1997.

 

MONTEIRO, Sergio C. L. Rios, de Almeida Prado: contribuições para uma interpretação pianística.Dissertação de Mestrado. Universidade Federal do Rio de Janeiro, 2000.

 

MOREIRA, Adriana L. da C. A poética nos 16 Poesilúdios para piano, de Almeida Prado.Dissertação de Mestrado. Universidade Estadual de Campinas, 2002.

 

RAMALHO, Rafael G. A imagem da arte da música: uma musicologia da Profecia nº 1, de Almeida Prado.Dissertação de Mestrado. Universidade do Rio de Janeiro, 2004.

 

ROCHA, Junia C. Decisões técnico-musicais e interpretativas no Segundo Caderno de Poesilúdios para piano, de Almeida Prado.Dissertação de Mestrado. Universidade Federal de Minas Gerias, 2004.

 

SANT’ANA, Edson, Hansen. Expressividade intervalar nos poesilúdios de Almeida Prado.Dissertação de Mestrado. Universidade de Brasília, 2009.

 

SILVA, Elizabete A. da. A temática religiosa em Le Rosaire de Medjugorjie – icône sonore pour piano, de Almeida Prado. Dissertação de Mestrado. Universidade Federal do Rio de Janeiro, 1994.

THYS, Marcelo Greenhalgh. A prática do piano a quatro mãos : problemas, soluções e sua aplicação ao estudo de peças de Almeida Prado e Ronaldo Miranda.Dissertação de Mestrado. Universidade Federal do Estado do Rio de Janeiro, 2007.

 

YANSEN, Carlos Alberto Silva. Almeida Prado: Estudos para piano, aspectos técnico-interpretativos.Dissertação de Mestrado. Universidade Estadual de Campinas, 2005.

 

 

Afterword

 

Almeida Prado’s Rhythmic Cartilha for the Piano is more than the name suggests – a true map of the piano language of a great Brazilian composer. His own definition is very significant: “This might be a Czerny for our days” – exercises that, due to their quality, even deserve the concert hall.

It all started with a request from Saloméa Gandelman, pianist and musicologist. She suggested to Almeida Prado that he should organize his complex rhythmic proposals in a manner that would make it easier for piano students to utilize a piece of work that has extremely precious moments, as the “Heavenly Letters”.

The composer accepted her suggestion, but this resulted in work that surpasses all expectations.  We find a piano language that unfolds in dizzying freedom, even if, at times, starting from traditional models: a Bach prelude, a “modinha” theme that suddenly transform themselves, so as to open up surprising rhythmic possibilities.  They seem improvisations, but the prevailing impression is that of an author discovering new routes.

The main goal is to start from rhythmic variations.  The author reviewed his contact with Hindemith, Messiaen, remembered Bela Bartok and his Mikrokosmos, he surveys Greek metrical models, but goes on to land on rhythms from non-European cultures, as the Afro-Brazilians and the Hindus.

Underneath the apparent simplicity, the biggest subtleties are hidden. He moves from the easiest beats, as 2/4, to the more complex ones as 10/16, 7/8 against 4/8, 15/12.    It is polirhythmics at work, with well-controlled beats variations.   The book is available with a CD, recording a good part of the exercises. 

With this musical macrocosm, Sara Cohen and Saloméa Gandelman achieved a most careful and competent production, allowing students and academic professionals to reach this fiery territory of our contemporary music.

 

Luiz Paulo Horta